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To make the cheesecake layer, preheat the oven to 350F and generously grease with nonstick cooking spray the bottom and sides of a 9-inch springform pan, preferably nonstick.
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Wrap the outside with aluminum foil, covering the bottom and extending all the way up the sides.
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Place 1 package of the cream cheese, 1/3 cup of the sugar, and the cornstarch in a large bowl and beat with an electric mixer on low speed until creamy, about 3 minutes, scraping the bowl down a couple of times.
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Blend in the remaining 2 packages cream cheese, 1 package at a time, scraping the bowl down after each.
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Raise the mixer speed to medium and beat in the remaining 1 cup sugar, and then the vanilla.
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Blend in the eggs, one at a time, beating well after adding each.
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Beat in the cream just until its completely blended.
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Do not overmix.
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Pour the batter into the prepared pan and place it in a large shallow pan.
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Add hot water to reach about 1 inch up the sides of the springform.
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Bake until the edges are light golden brown and the top is light golden tan, about 1 1/4 hours.
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Remove the springform from the water bath, transfer it to a wire rack, and cool for 2 hours.
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Then cover the pan with plastic wrap and refrigerate until completely cold, about 4 hours.
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Place in the freezer until ready to assemble the cake.
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To make the chocolate layer, preheat the oven to 350F if necessary.
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Butter and flour or generously grease with nonstick cooking spray the bottom and sides of three 9-inch round cake pans.
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Line the bottom of each pan with a round of parchment or waxed paper.
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Sift the flour, baking powder, and salt together into a medium bowl.
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In a large bowl, beat the butter and both sugars together with an electric mixer on medium speed until light yellow and creamy.
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Add the egg yolks, one at a time, beating well after each.
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Beat in the melted chocolate and the vanilla.
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Using a wooden spoon, stir in the flour mixture, alternating with the milk, mixing well after each until blended.
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Put the egg whites and cream of tartar in a clean bowl and beat on high speed until stiff (but not dry) peaks form.
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Fold about one-third of the whites into the chocolate batter; then gently fold in the remaining whites.
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Dont worry if you still see a few white speckstheyll disappear during baking.
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Divide the batter evenly among the prepared cake pans.
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Bake until a toothpick inserted in the center comes out with moist crumbs clinging to it, about 30 minutes.
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Cool the cakes in the pans on a wire rack for 15 minutes.
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Then remove the cakes from the pans and gently peel off the paper liners.
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Let cool completely, about 2 hours.
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Then cover with plastic wrap and refrigerate overnight or until ready to assemble the cake.
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To make the frosting, sift the confectioners sugar, cocoa powder, and salt together into a large bowl.
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In another large bowl, beat the butter with an electric mixer on high speed until light yellow and slightly thickened, about 3 minutes.
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With the mixer still running, beat in the chocolate, corn syrup, and vanilla.
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Reduce the mixer speed to low and beat in the sugar-cocoa mixture in two additions, beating well after each.
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Blend in the cream until the frosting has a spreading consistency, adding a little more cream if needed.
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Whip the frosting on high speed until light and creamy, about 2 minutes.
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Remove the cheesecake from the freezer and let stand at room temperature for 10 minutes.
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Place 1 layer of devils food cake, top side down, on a cake plate and spread some of the frosting over the top.
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Release and remove the ring of the springform; then remove the frozen cheesecake from the bottom of the pan.
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Place the cheesecake, top side down, on the frosted cake layer and spread some frosting over it.
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Top with the second devils food layer, top side down.
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Spread with more frosting and cover with the third devils food layer, top side up.
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Frost the sides and top of the cake with the remaining frosting.
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Decorate with the chocolate curls.
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Refrigerate for at least 2 hours to allow the cheesecake to thaw enough to slice easily.
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Use a sharp straight-edge knife, not a serrated one, to cut into slices.
